Abstract: By means of the global sub-iterative solution of fluid dynamic equations and rigid-body dynamic equations (CFD/RBD), a coupling numerical method is proposed to investigate the self-excited unsteady planar motion of a flight vehicle with two degrees of freedom, i.e., free pitching and free vertical motion. The numerical result shows that the unstable free planar motion of a flared cone-cylinder configuration develops a limit-cycle motion in the supersonic flow accompanied by the unsteady evolutions of the flow structure. The free planar oscillation maintains the major characteristics of free pitching, but with smaller amplitudes and higher frequencies. In addition, the vehicle in the free planar motion seems to turn around a fixed point near the nose of the vehicle. The nonlinear dynamic equation characterizing the hysteresis is deduced based on the second Lagrange equation and the principle of virtual work, and the parameterized motion is analyzed approximately by the multiple time scales (MTS) method. The self-oscillation is a quasi simple harmonic motion. The damping at the balance point is the bifurcation parameter that determines its dynamic stability. The amplitude is associated with the nonlinear damping and the frequency is correlated with the nonlinear rigidity. Theoretical analysis vali-dates the “fixed point” of the vehicle in free planar motion and in a self-consistent way makes clear why the oscillation amplitude becomes smaller with the additive vertical motion. It provides validation for the modeling method, with whose CFD results the theoretical analysis and numerical reconstruction agree well.

Key words: unsteady flow, dynamic stability, global sub-iteration, nonlinear dynamics model, coupling motion